Mechanical Properties of Rectangular Cold-Formed Steel Tube Concrete Columns

Literature Overview

The paper published in Engineering Mechanics (Vol. 23, Issue 3, 2006, pp. 147–155) by Tao Zhong, Wang Zhibin, and Han Linhai from Fuzhou University and Tsinghua University presents a comprehensive study on the mechanical behaviour of rectangular cold-formed steel tube concrete (RCF-SC) columns. This research is particularly significant because cold-formed steel sections offer substantial economic and structural advantages over hot-rolled sections, yet their interaction with concrete cores has been less thoroughly investigated.

Cold-Formed Steel Sections: Advantages and Challenges

Advantages of Cold-Formed Steel

Cold-formed steel sections are produced by rolling hot-rolled coils at room temperature through a series of roll forming stations. Compared to hot-rolled sections, cold-formed sections offer the following advantages:

• Higher strength-to-weight ratio due to the work hardening effect during cold forming
• Wider range of available section dimensions and shapes
• Lower material waste and manufacturing cost
• Better surface finish and dimensional accuracy
• Reduced carbon footprint in production

Challenges in Concrete-Filled Application

However, the use of cold-formed steel in concrete-filled applications introduces several challenges:

• The residual stresses from the cold-forming process affect the local buckling behaviour
• The sharp corners of cold-formed sections may lead to stress concentrations
• The material properties may vary along the section due to differential strain hardening
• The standard design methods developed for hot-rolled sections may not be directly applicable

Experimental Programme

The study involved 8 cold-formed steel tube concrete specimens subjected to different loading conditions:

The specimens were instrumented with strain gauges to measure the local behaviour of the steel tube and the concrete core. The load-deformation relationships were recorded throughout the entire loading process, from the elastic range through yielding to post-peak behaviour.

Constitutive Model Development

Steel Stress-Strain Relationship

The stress-strain relationship for cold-formed steel accounts for the work hardening effect and the residual stress distribution:

• The elastic modulus is taken as 206 GPa, consistent with standard carbon steel.
• The yield stress is determined from the coupon test results, with consideration of the strain hardening effect.
• The strain hardening exponent is calibrated from the experimental data to capture the post-yield behaviour accurately.

Concrete Stress-Strain Relationship

The confined concrete stress-strain relationship follows the Mander model, modified for the rectangular section geometry:

• The confined concrete strength is enhanced by the lateral confinement pressure from the steel tube.
• The confinement pressure is calculated based on the equilibrium of forces in the steel tube.
• The ultimate strain of the confined concrete is increased proportionally to the confinement level.

Numerical Analysis and Validation

The authors developed a numerical analysis method using a numerical solution approach to solve the equilibrium equations for the composite cross-section. The method accounts for:

1. The nonlinear stress-strain relationships of both steel and concrete
2. The interaction between the steel tube and the concrete core
3. The geometric nonlinearity due to large deformations
4. The slenderness effects on the load-bearing capacity

The numerical results showed good agreement with the experimental results for all three loading conditions (axial compression, pure bending, and combined compression-bending). The load-deformation curves predicted by the numerical model matched the experimental curves within an acceptable error margin, validating the constitutive models and the numerical solution method.

Practical Design Formulas

Based on the parametric analysis, the authors provided practical design formulas for the load-bearing capacity of RCF-SC columns under different loading conditions:

The design formulas are presented in a practical form that can be directly incorporated into design codes or used in engineering practice. The parametric analysis revealed the following trends:

• The load-bearing capacity increases with increasing steel ratio, but the rate of increase diminishes at higher steel ratios.
• The slenderness ratio has a significant effect on the axial compression capacity, with slender columns exhibiting a more pronounced strength reduction.
• The concrete strength has a moderate effect on the overall capacity, as the steel tube contributes significantly to the load-bearing capacity.

Engineering Practice Implications

Material Selection

For engineers considering cold-formed steel tube concrete columns, the following material selection guidelines are recommended:

1. The cold-formed steel grade should be selected to ensure adequate ductility for the confinement function. Grades with elongation greater than 20% are preferred.
2. The concrete grade should be selected to provide adequate strength while maintaining workability for pouring inside the steel tube. Concrete grades ranging from C30 to C60 are suitable.
3. The steel-to-concrete strength ratio should be optimised to achieve the best composite action. A ratio in the range of 1.5–3.0 is generally recommended.

Construction Considerations

The construction of cold-formed steel tube concrete columns requires special attention to the following aspects:

• The steel tube must be inspected for dimensional accuracy and surface defects before concrete filling.
• The concrete pouring must be done in controlled lifts to prevent segregation and ensure uniform filling.
• The vibration of concrete must be carefully controlled to avoid damaging the cold-formed steel tube, particularly at the corners.
• The curing regime must be adequate to ensure proper concrete strength development, especially in the early stages.

Key Questions and Reflections

Several aspects of this study merit further consideration. First, the effect of the cold-forming residual stresses on the long-term behaviour of the composite column is not addressed. Residual stresses can affect the buckling behaviour and the fatigue performance, which are important for columns subjected to cyclic loading. Second, the study focuses on rectangular sections, but the principles can be extended to other cold-formed section shapes, such as circular, elliptical, and thin-walled open sections. Third, the fire resistance of cold-formed steel tube concrete columns is not examined, yet fire protection is a critical design consideration for building structures. The cold-formed steel may lose strength at lower temperatures than hot-rolled steel due to the work hardening effect, which could affect the fire resistance performance.

Study Insights and Implications

The most valuable contribution of this paper is the demonstration that cold-formed steel tube concrete columns can achieve mechanical performance comparable to or better than hot-rolled steel tube concrete columns, while offering significant economic advantages. The practical design formulas provided by the authors make it possible for engineers to adopt this technology in practice without requiring complex numerical analysis for routine design. The research also highlights the importance of understanding the constitutive behaviour of both materials in the composite system, as the interaction between the steel and concrete is the key to achieving the full composite action. For the steel pipe manufacturing industry, this research validates the use of cold-formed steel tubes in structural applications and opens up new market opportunities for cold-formed steel pipe producers. The work by Tao Zhong, Wang Zhibin, and Han Linhai represents a significant contribution to the advancement of composite structural engineering and should be referenced by any engineer considering cold-formed steel tube concrete systems.